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A309471
Sum of the prime parts in the partitions of n into 10 parts.
7
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 7, 11, 28, 41, 79, 115, 191, 273, 428, 574, 851, 1133, 1576, 2072, 2819, 3621, 4812, 6112, 7918, 9931, 12655, 15684, 19714, 24221, 29987, 36534, 44796, 54051, 65660, 78684, 94653, 112671, 134499, 159012, 188569, 221650
OFFSET
0,12
FORMULA
a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} (r * c(r) + q * c(q) + p * c(p) + o * c(o) + m * c(m) + l * c(l) + k * c(k) + j * c(j) + i * c(i) + (n-i-j-k-l-m-o-p-q-r) * c(n-i-j-k-l-m-o-p-q-r)), where c is the prime characteristic (A010051).
MATHEMATICA
Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[i (PrimePi[i] - PrimePi[i - 1]) + j (PrimePi[j] - PrimePi[j - 1]) + k (PrimePi[k] - PrimePi[k - 1]) + l (PrimePi[l] - PrimePi[l - 1]) + m (PrimePi[m] - PrimePi[m - 1]) + o (PrimePi[o] - PrimePi[o - 1]) + p (PrimePi[p] - PrimePi[p - 1]) + q (PrimePi[q] - PrimePi[q - 1]) + r (PrimePi[r] - PrimePi[r - 1]) + (n - i - j - k - l - m - o - p - q - r) (PrimePi[n - i - j - k - l - m - o - p - q - r] - PrimePi[n - i - j - k - l - m - o - p - q - r - 1]), {i, j, Floor[(n - j - k - l - m - o - p - q - r)/2]}], {j, k, Floor[(n - k - l - m - o - p - q - r)/3]}], {k, l, Floor[(n - l - m - o - p - q - r)/4]}], {l, m, Floor[(n - m - o - p - q - r)/5]}], {m, o, Floor[(n - o - p - q - r)/6]}], {o, p, Floor[(n - p - q - r)/7]}], {p, q, Floor[(n - q - r)/8]}], {q, r, Floor[(n - r)/9]}], {r, Floor[n/10]}], {n, 0, 80}]
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 03 2019
STATUS
approved